R Notebook

Call Libraries

library(tidyverse)
library(car)
library(moments)
library(glmnet)

Calling the Transformed Datasets

income_cleaned = read_csv('Shiny_app/data/income_cleaned.csv')
industry_cleaned = read_csv('Shiny_app/data/industry_cleaned.csv')

Creating the Models

sat.model.summary <- function (df, field, sat.formula){
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print('kurtosis')
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ .
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.17297, p-value < 2.2e-16

[1] "kurtosis"
[1] 172.7518

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11338570   -547702     94139    421302  87181761 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -1.157e+08  5.512e+07  -2.100  0.03590 *  
Year                                                                                           5.721e+04  2.731e+04   2.095  0.03634 *  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -3.287e+05  1.242e+06  -0.265  0.79140    
NameAlternative Minimum Tax Credit                                                             6.538e+05  9.757e+05   0.670  0.50286    
NameBeer Production Credit                                                                     3.316e+05  1.290e+06   0.257  0.79715    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.429e+06  9.960e+05   1.434  0.15162    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.098e+06  1.421e+06   2.883  0.00398 ** 
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.182e+06  9.927e+05   1.191  0.23386    
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                             -7.587e+04  9.920e+05  -0.076  0.93904    
NameClean Heating Fuel Credit                                                                  7.148e+04  1.024e+06   0.070  0.94436    
NameConservation Easement Tax Credit                                                           1.143e+05  1.064e+06   0.107  0.91444    
NameCredit for Employment of Persons with Disabilities                                        -9.343e+05  1.119e+06  -0.835  0.40391    
NameCredit for Purchase of an Automated External Defibrillator                                -1.449e+05  9.695e+05  -0.150  0.88117    
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.316e+05  1.779e+06   0.130  0.89645    
NameEmpire State Apprentice Tax Credit                                                        -7.983e+05  1.524e+06  -0.524  0.60040    
NameEmpire State Commercial Production Credit                                                  2.183e+05  1.291e+06   0.169  0.86576    
NameEmpire State Film Post Production Credit                                                   2.521e+04  1.049e+06   0.024  0.98082    
NameEmpire State Film Production Credit                                                        1.145e+07  9.967e+05  11.485  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                     -2.342e+05  1.775e+06  -0.132  0.89507    
NameExcelsior Jobs Program Credit                                                              1.035e+05  9.545e+05   0.108  0.91366    
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             2.752e+06  8.862e+05   3.105  0.00193 ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   4.845e+05  9.213e+05   0.526  0.59899    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.245e+06  9.239e+05   1.348  0.17785    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners          -1.025e+05  9.549e+05  -0.107  0.91455    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -6.145e+04  9.387e+05  -0.065  0.94781    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     9.119e+04  1.044e+06   0.087  0.93038    
NameFarm Workforce Retention Credit                                                           -7.802e+03  1.285e+06  -0.006  0.99516    
NameFarmers' School Tax Credit                                                                 1.440e+05  1.021e+06   0.141  0.88786    
NameHire a Veteran Credit                                                                     -1.238e+06  1.782e+06  -0.695  0.48721    
NameHistoric Properties Rehabilitation Credit                                                  1.352e+06  1.055e+06   1.282  0.20015    
NameIndustrial or Manufacturing Business Tax Credit                                            4.997e+05  1.074e+06   0.465  0.64173    
NameInvestment Tax Credit                                                                      4.463e+05  8.895e+05   0.502  0.61588    
NameInvestment Tax Credit for the Financial Services Industry                                  3.976e+05  1.008e+06   0.395  0.69325    
NameLife Sciences Research & Development Tax Credit                                           -8.207e+04  2.099e+06  -0.039  0.96882    
NameLong-Term Care Insurance Credit                                                            1.246e+05  9.808e+05   0.127  0.89892    
NameLow-Income Housing Credit                                                                 -2.764e+04  1.113e+06  -0.025  0.98020    
NameMinimum Wage Reimbursement Credit                                                         -2.931e+05  1.006e+06  -0.291  0.77075    
NameMortgage Servicing Tax Credit                                                             -4.540e+05  1.085e+06  -0.418  0.67565    
NameNew York Youth Jobs Program Tax Credit                                                    -2.587e+05  9.381e+05  -0.276  0.78279    
NameQETC Capital Tax Credit                                                                    2.616e+05  1.386e+06   0.189  0.85032    
NameQETC Employment Credit                                                                     1.335e+05  1.026e+06   0.130  0.89641    
NameQETC Facilities, Operations, and Training Credit                                           5.153e+05  1.918e+06   0.269  0.78820    
NameReal Property Tax Relief Credit for Manufacturing                                         -2.635e+05  9.654e+05  -0.273  0.78490    
NameSpecial Additional Mortgage Recording Tax Credit                                           3.678e+04  9.244e+05   0.040  0.96827    
NameSTART-UP NY Tax Elimination Credit                                                         4.061e+03  1.130e+06   0.004  0.99713    
Group1,000,000 - 24,999,999                                                                    2.170e+05  3.501e+05   0.620  0.53548    
Group100,000 - 499,999                                                                         1.352e+05  3.579e+05   0.378  0.70572    
Group100,000,000 - 499,999,999                                                                 9.644e+05  3.937e+05   2.449  0.01441 *  
Group25,000,000 - 49,999,999                                                                   4.519e+05  4.223e+05   1.070  0.28474    
Group50,000,000 - 99,999,999                                                                   4.021e+05  4.235e+05   0.950  0.34247    
Group500,000 - 999,999                                                                         2.195e+05  3.880e+05   0.566  0.57170    
Group500,000,000 - and over                                                                    3.073e+06  3.846e+05   7.991 2.33e-15 ***
GroupZero or Net Loss                                                                          9.536e+05  3.339e+05   2.856  0.00433 ** 
Num                                                                                           -4.520e+02  8.569e+02  -0.527  0.59791    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3868000 on 1867 degrees of freedom
Multiple R-squared:  0.2361,    Adjusted R-squared:  0.2144 
F-statistic: 10.88 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

income.model <- lm(sat.formula, data = income_cleaned)

sat.model.summary(industry_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.22287, p-value < 2.2e-16

[1] "kurtosis"
[1] 138.5482

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11581741   -371031    -23164    154182  28917959 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -3.926e+07  2.051e+07  -1.914 0.055677 .  
Year                                                                                           1.936e+04  1.016e+04   1.905 0.056959 .  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          5.584e+04  5.062e+05   0.110 0.912180    
NameAlternative Minimum Tax Credit                                                             3.523e+05  4.208e+05   0.837 0.402556    
NameBeer Production Credit                                                                     8.799e+04  6.261e+05   0.141 0.888249    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.919e+06  4.473e+05   4.290 1.86e-05 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.064e+06  7.278e+05   5.584 2.62e-08 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.054e+06  4.779e+05   2.206 0.027462 *  
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              1.327e+05  4.760e+05   0.279 0.780429    
NameClean Heating Fuel Credit                                                                  2.785e+05  4.595e+05   0.606 0.544549    
NameConservation Easement Tax Credit                                                           2.743e+04  4.700e+05   0.058 0.953457    
NameCredit for Employment of Persons with Disabilities                                         1.574e+05  5.069e+05   0.311 0.756142    
NameCredit for Purchase of an Automated External Defibrillator                                 1.082e+05  4.465e+05   0.242 0.808639    
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.090e+05  8.286e+05   0.252 0.800866    
NameEmpire State Apprentice Tax Credit                                                        -3.324e+05  1.012e+06  -0.329 0.742537    
NameEmpire State Commercial Production Credit                                                  3.524e+05  6.172e+05   0.571 0.568123    
NameEmpire State Film Post Production Credit                                                   5.332e+05  5.224e+05   1.021 0.307585    
NameEmpire State Film Production Credit                                                        1.170e+07  4.785e+05  24.458  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      7.676e+04  9.010e+05   0.085 0.932112    
NameExcelsior Jobs Program Credit                                                              7.086e+05  4.393e+05   1.613 0.106849    
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.381e+06  4.318e+05   3.199 0.001399 ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   3.715e+05  4.213e+05   0.882 0.377942    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.160e+06  4.192e+05   2.767 0.005700 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           3.634e+05  4.311e+05   0.843 0.399359    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            2.567e+05  4.265e+05   0.602 0.547350    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     7.379e+04  5.041e+05   0.146 0.883634    
NameFarm Workforce Retention Credit                                                            2.727e+04  5.352e+05   0.051 0.959361    
NameFarmers' School Tax Credit                                                                 1.287e+05  5.133e+05   0.251 0.802102    
NameHire a Veteran Credit                                                                      1.459e+05  8.253e+05   0.177 0.859709    
NameHistoric Properties Rehabilitation Credit                                                  1.875e+06  4.841e+05   3.874 0.000110 ***
NameInvestment Tax Credit                                                                      7.182e+05  4.129e+05   1.739 0.082075 .  
NameInvestment Tax Credit for the Financial Services Industry                                  6.339e+05  5.757e+05   1.101 0.270913    
NameLife Sciences Research & Development Tax Credit                                           -2.243e+03  9.007e+05  -0.002 0.998014    
NameLong-Term Care Insurance Credit                                                            1.385e+05  4.200e+05   0.330 0.741537    
NameLow-Income Housing Credit                                                                  1.642e+06  5.494e+05   2.988 0.002833 ** 
NameMinimum Wage Reimbursement Credit                                                          9.624e+04  4.381e+05   0.220 0.826159    
NameMortgage Servicing Tax Credit                                                              2.077e+05  6.462e+05   0.321 0.747934    
NameNew York Youth Jobs Program Tax Credit                                                     1.953e+05  4.273e+05   0.457 0.647604    
NameQETC Capital Tax Credit                                                                    2.986e+05  5.868e+05   0.509 0.610823    
NameQETC Employment Credit                                                                     8.982e+04  4.465e+05   0.201 0.840607    
NameQETC Facilities, Operations, and Training Credit                                           3.477e+05  6.711e+05   0.518 0.604441    
NameReal Property Tax Relief Credit for Manufacturing                                          1.520e+05  4.423e+05   0.344 0.731171    
NameSpecial Additional Mortgage Recording Tax Credit                                           2.609e+05  4.432e+05   0.589 0.556155    
NameSTART-UP NY Tax Elimination Credit                                                         1.703e+04  4.750e+05   0.036 0.971411    
GroupAdministrative and Support and Waste Management and Remediation Services                 -2.280e+03  2.519e+05  -0.009 0.992777    
GroupAdministrative/Support/Waste Management/Remediation Services                             -3.173e+03  2.798e+05  -0.011 0.990952    
GroupAgriculture, Forestry, Fishing and Hunting                                                7.269e+04  2.330e+05   0.312 0.755097    
GroupArts, Entertainment, and Recreation                                                       5.866e+05  2.317e+05   2.532 0.011408 *  
GroupConstruction                                                                             -1.699e+04  2.171e+05  -0.078 0.937621    
GroupEducational Services                                                                      5.569e+04  2.948e+05   0.189 0.850176    
GroupFinance and Insurance                                                                     2.139e+05  2.034e+05   1.051 0.293237    
GroupHealth Care and Social Assistance                                                         1.300e+04  2.290e+05   0.057 0.954731    
GroupInformation                                                                              -2.433e+05  2.178e+05  -1.117 0.263917    
GroupManagement of Companies and Enterprises                                                   3.355e+05  1.949e+05   1.721 0.085332 .  
GroupManufacturing                                                                             6.786e+05  2.028e+05   3.346 0.000831 ***
GroupMining                                                                                   -1.561e+04  3.593e+05  -0.043 0.965352    
GroupMining, Quarrying, and Oil and Gas Extraction                                             1.084e+05  3.011e+05   0.360 0.718901    
GroupOther Services (except Public Administration)                                            -6.462e+04  2.217e+05  -0.291 0.770697    
GroupProfessional, Scientific, and Technical Services                                          3.736e+05  2.085e+05   1.792 0.073214 .  
GroupReal Estate and Rental and Leasing                                                        9.506e+04  2.044e+05   0.465 0.641882    
GroupRetail Trade                                                                              4.746e+04  2.036e+05   0.233 0.815756    
GroupTransportation and Warehousing                                                           -1.866e+04  2.300e+05  -0.081 0.935321    
GroupUtilities                                                                                 5.308e+05  2.633e+05   2.016 0.043917 *  
GroupWholesale Trade                                                                           6.106e+04  2.081e+05   0.293 0.769261    
Num                                                                                           -9.657e+02  4.272e+02  -2.260 0.023889 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1612000 on 2411 degrees of freedom
Multiple R-squared:  0.4674,    Adjusted R-squared:  0.4533 
F-statistic: 33.06 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

industry.model <- lm(sat.formula, data = industry_cleaned)

Selecting Specific Diagnostic plots for linear models

plot(income.model, which = 1)

plot(income.model, which = 2)

plot(income.model, which = 3)

plot(income.model, which = 5)

Correcting violation of Normality in previous model with BoxCox transform

bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}

#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))

income.lambda.bc

[1] -0.01414141

#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))

industry.lambda.bc

[1] -0.03434343

bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg))) #took out field Amount
}

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)

Testing out bc_func for migration to Shiny App global.R file

bc_funct <- function (df, lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  lambda.bc = bc$x[which(bc$y == max(bc$y))]
  return(df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg)))
}

bc_funct(income_cleaned, income.model, seq(-0.2, 0.2, 1/10))

bc_func2 <- function (){
  bc = boxCox(lm(Avg ~ ., data = industry_cleaned), lambda = seq(-0.2, 0.2, 1/10))
  lambda.bc = bc$x[which(bc$y == max(bc$y))]
  return(industry_cleaned %>%
           mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>%
           select(-c(Avg)))
}

industry_cleaned_bc <-bc_func2()
industry_cleaned_bc

Checking linear regression assumptions for the transformed data.

sat.formula.bc <- Avg.bc ~ .
sat.field.bc <- 'Avg.bc'

#Income
sat.model.summary(income_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.99696, p-value = 0.000782

[1] "kurtosis"
[1] 2.744669

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.6597 -0.5738 -0.0113  0.5668  4.4826 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -3.634e+01  1.456e+01  -2.496 0.012643 *  
Year                                                                                           2.288e-02  7.214e-03   3.171 0.001543 ** 
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -8.643e-01  3.281e-01  -2.634 0.008510 ** 
NameAlternative Minimum Tax Credit                                                            -2.052e+00  2.577e-01  -7.962 2.91e-15 ***
NameBeer Production Credit                                                                     5.687e-01  3.407e-01   1.669 0.095234 .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.715e+00  2.630e-01   6.521 8.99e-11 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.676e+00  3.754e-01   7.130 1.43e-12 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.331e+00  2.622e-01   5.076 4.24e-07 ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              5.458e-02  2.620e-01   0.208 0.834991    
NameClean Heating Fuel Credit                                                                 -3.086e+00  2.705e-01 -11.409  < 2e-16 ***
NameConservation Easement Tax Credit                                                          -2.137e+00  2.810e-01  -7.606 4.45e-14 ***
NameCredit for Employment of Persons with Disabilities                                        -3.118e+00  2.956e-01 -10.547  < 2e-16 ***
NameCredit for Purchase of an Automated External Defibrillator                                -2.938e+00  2.560e-01 -11.473  < 2e-16 ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -5.673e-01  4.698e-01  -1.207 0.227430    
NameEmpire State Apprentice Tax Credit                                                        -2.207e+00  4.024e-01  -5.485 4.71e-08 ***
NameEmpire State Commercial Production Credit                                                  6.075e-02  3.410e-01   0.178 0.858634    
NameEmpire State Film Post Production Credit                                                   1.101e+00  2.769e-01   3.977 7.25e-05 ***
NameEmpire State Film Production Credit                                                        2.853e+00  2.632e-01  10.838  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      2.508e-01  4.688e-01   0.535 0.592803    
NameExcelsior Jobs Program Credit                                                              4.651e-01  2.521e-01   1.845 0.065178 .  
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             8.876e-01  2.341e-01   3.792 0.000154 ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   1.775e-01  2.433e-01   0.730 0.465701    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.220e+00  2.440e-01   5.000 6.26e-07 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           1.182e-01  2.522e-01   0.469 0.639260    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -8.497e-01  2.479e-01  -3.427 0.000623 ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -1.358e+00  2.756e-01  -4.928 9.02e-07 ***
NameFarm Workforce Retention Credit                                                           -1.612e+00  3.394e-01  -4.749 2.20e-06 ***
NameFarmers' School Tax Credit                                                                -1.311e+00  2.696e-01  -4.863 1.26e-06 ***
NameHire a Veteran Credit                                                                     -2.915e+00  4.706e-01  -6.195 7.15e-10 ***
NameHistoric Properties Rehabilitation Credit                                                  1.918e+00  2.786e-01   6.886 7.81e-12 ***
NameIndustrial or Manufacturing Business Tax Credit                                           -1.718e+00  2.836e-01  -6.059 1.66e-09 ***
NameInvestment Tax Credit                                                                      7.147e-02  2.349e-01   0.304 0.760985    
NameInvestment Tax Credit for the Financial Services Industry                                  3.176e-01  2.662e-01   1.193 0.232870    
NameLife Sciences Research & Development Tax Credit                                            7.033e-01  5.543e-01   1.269 0.204728    
NameLong-Term Care Insurance Credit                                                           -2.863e+00  2.590e-01 -11.051  < 2e-16 ***
NameLow-Income Housing Credit                                                                 -9.063e-01  2.940e-01  -3.083 0.002080 ** 
NameMinimum Wage Reimbursement Credit                                                         -1.241e+00  2.656e-01  -4.674 3.17e-06 ***
NameMortgage Servicing Tax Credit                                                             -9.378e-01  2.865e-01  -3.273 0.001084 ** 
NameNew York Youth Jobs Program Tax Credit                                                    -1.330e+00  2.478e-01  -5.367 9.01e-08 ***
NameQETC Capital Tax Credit                                                                    4.561e-01  3.661e-01   1.246 0.212956    
NameQETC Employment Credit                                                                    -5.888e-01  2.709e-01  -2.174 0.029855 *  
NameQETC Facilities, Operations, and Training Credit                                           5.799e-01  5.065e-01   1.145 0.252462    
NameReal Property Tax Relief Credit for Manufacturing                                         -1.518e+00  2.550e-01  -5.956 3.09e-09 ***
NameSpecial Additional Mortgage Recording Tax Credit                                          -2.309e-01  2.441e-01  -0.946 0.344374    
NameSTART-UP NY Tax Elimination Credit                                                        -2.193e+00  2.985e-01  -7.345 3.05e-13 ***
Group1,000,000 - 24,999,999                                                                    1.090e+00  9.246e-02  11.785  < 2e-16 ***
Group100,000 - 499,999                                                                         3.590e-01  9.451e-02   3.798 0.000150 ***
Group100,000,000 - 499,999,999                                                                 1.685e+00  1.040e-01  16.202  < 2e-16 ***
Group25,000,000 - 49,999,999                                                                   1.325e+00  1.115e-01  11.883  < 2e-16 ***
Group50,000,000 - 99,999,999                                                                   1.473e+00  1.118e-01  13.172  < 2e-16 ***
Group500,000 - 999,999                                                                         6.032e-01  1.025e-01   5.886 4.67e-09 ***
Group500,000,000 - and over                                                                    2.332e+00  1.016e-01  22.953  < 2e-16 ***
GroupZero or Net Loss                                                                          9.934e-01  8.817e-02  11.267  < 2e-16 ***
Num                                                                                           -1.533e-03  2.263e-04  -6.775 1.66e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.022 on 1867 degrees of freedom
Multiple R-squared:  0.7368,    Adjusted R-squared:  0.7293 
F-statistic: 98.61 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

#Industry
sat.model.summary(industry_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.9902, p-value = 5.826e-12

[1] "kurtosis"
[1] 2.513097

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2888 -0.4697  0.0183  0.4928  3.9068 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -6.095e+01  1.107e+01  -5.505 4.09e-08 ***
Year                                                                                           3.440e-02  5.488e-03   6.269 4.30e-10 ***
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          2.665e-01  2.733e-01   0.975 0.329737    
NameAlternative Minimum Tax Credit                                                            -2.463e+00  2.272e-01 -10.839  < 2e-16 ***
NameBeer Production Credit                                                                     6.334e-01  3.381e-01   1.873 0.061126 .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  2.198e+00  2.415e-01   9.100  < 2e-16 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.727e+00  3.930e-01   6.939 5.06e-12 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.586e+00  2.581e-01   6.148 9.17e-10 ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              9.695e-01  2.570e-01   3.772 0.000166 ***
NameClean Heating Fuel Credit                                                                 -2.544e+00  2.481e-01 -10.252  < 2e-16 ***
NameConservation Easement Tax Credit                                                          -1.123e+00  2.538e-01  -4.423 1.02e-05 ***
NameCredit for Employment of Persons with Disabilities                                        -1.245e+00  2.737e-01  -4.549 5.67e-06 ***
NameCredit for Purchase of an Automated External Defibrillator                                -1.535e+00  2.411e-01  -6.368 2.29e-10 ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -8.171e-02  4.474e-01  -0.183 0.855119    
NameEmpire State Apprentice Tax Credit                                                        -8.683e-01  5.464e-01  -1.589 0.112125    
NameEmpire State Commercial Production Credit                                                  6.235e-01  3.333e-01   1.871 0.061481 .  
NameEmpire State Film Post Production Credit                                                   1.439e+00  2.821e-01   5.100 3.66e-07 ***
NameEmpire State Film Production Credit                                                        3.232e+00  2.584e-01  12.509  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      1.012e+00  4.865e-01   2.080 0.037608 *  
NameExcelsior Jobs Program Credit                                                              1.643e+00  2.372e-01   6.929 5.42e-12 ***
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.310e+00  2.332e-01   5.617 2.17e-08 ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   7.127e-01  2.275e-01   3.133 0.001750 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.707e+00  2.264e-01   7.540 6.61e-14 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           9.777e-01  2.328e-01   4.200 2.77e-05 ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            1.609e-01  2.303e-01   0.699 0.484921    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -5.241e-01  2.722e-01  -1.925 0.054320 .  
NameFarm Workforce Retention Credit                                                           -8.623e-01  2.890e-01  -2.984 0.002876 ** 
NameFarmers' School Tax Credit                                                                -1.158e+00  2.771e-01  -4.179 3.03e-05 ***
NameHire a Veteran Credit                                                                     -1.040e+00  4.456e-01  -2.335 0.019638 *  
NameHistoric Properties Rehabilitation Credit                                                  2.397e+00  2.614e-01   9.172  < 2e-16 ***
NameInvestment Tax Credit                                                                      6.981e-01  2.230e-01   3.131 0.001763 ** 
NameInvestment Tax Credit for the Financial Services Industry                                  1.560e+00  3.108e-01   5.019 5.59e-07 ***
NameLife Sciences Research & Development Tax Credit                                            9.057e-01  4.864e-01   1.862 0.062697 .  
NameLong-Term Care Insurance Credit                                                           -1.867e+00  2.268e-01  -8.231 3.01e-16 ***
NameLow-Income Housing Credit                                                                  1.331e+00  2.967e-01   4.487 7.57e-06 ***
NameMinimum Wage Reimbursement Credit                                                         -9.161e-01  2.366e-01  -3.872 0.000111 ***
NameMortgage Servicing Tax Credit                                                              8.932e-01  3.489e-01   2.560 0.010534 *  
NameNew York Youth Jobs Program Tax Credit                                                     1.263e-01  2.307e-01   0.548 0.584069    
NameQETC Capital Tax Credit                                                                    1.162e+00  3.168e-01   3.667 0.000251 ***
NameQETC Employment Credit                                                                    -3.048e-01  2.411e-01  -1.264 0.206249    
NameQETC Facilities, Operations, and Training Credit                                           1.147e+00  3.624e-01   3.165 0.001571 ** 
NameReal Property Tax Relief Credit for Manufacturing                                         -6.559e-01  2.388e-01  -2.746 0.006077 ** 
NameSpecial Additional Mortgage Recording Tax Credit                                           7.505e-01  2.393e-01   3.136 0.001736 ** 
NameSTART-UP NY Tax Elimination Credit                                                        -1.834e+00  2.565e-01  -7.151 1.14e-12 ***
GroupAdministrative and Support and Waste Management and Remediation Services                  2.878e-01  1.360e-01   2.116 0.034417 *  
GroupAdministrative/Support/Waste Management/Remediation Services                              1.675e-01  1.511e-01   1.109 0.267612    
GroupAgriculture, Forestry, Fishing and Hunting                                               -1.132e-01  1.258e-01  -0.899 0.368486    
GroupArts, Entertainment, and Recreation                                                       5.595e-01  1.251e-01   4.473 8.09e-06 ***
GroupConstruction                                                                             -4.299e-02  1.172e-01  -0.367 0.713860    
GroupEducational Services                                                                      2.253e-01  1.592e-01   1.415 0.157160    
GroupFinance and Insurance                                                                     5.350e-01  1.099e-01   4.870 1.19e-06 ***
GroupHealth Care and Social Assistance                                                        -6.777e-02  1.237e-01  -0.548 0.583720    
GroupInformation                                                                               7.098e-01  1.176e-01   6.037 1.81e-09 ***
GroupManagement of Companies and Enterprises                                                   6.672e-01  1.052e-01   6.340 2.73e-10 ***
GroupManufacturing                                                                             4.608e-01  1.095e-01   4.208 2.67e-05 ***
GroupMining                                                                                    2.515e-01  1.940e-01   1.296 0.194977    
GroupMining, Quarrying, and Oil and Gas Extraction                                             3.869e-01  1.626e-01   2.379 0.017421 *  
GroupOther Services (except Public Administration)                                            -1.550e-01  1.197e-01  -1.295 0.195482    
GroupProfessional, Scientific, and Technical Services                                          4.875e-01  1.126e-01   4.331 1.55e-05 ***
GroupReal Estate and Rental and Leasing                                                        1.461e-01  1.104e-01   1.324 0.185596    
GroupRetail Trade                                                                              3.754e-01  1.100e-01   3.414 0.000650 ***
GroupTransportation and Warehousing                                                            2.125e-01  1.242e-01   1.711 0.087179 .  
GroupUtilities                                                                                 6.972e-01  1.422e-01   4.904 1.00e-06 ***
GroupWholesale Trade                                                                           4.367e-01  1.124e-01   3.886 0.000105 ***
Num                                                                                            4.542e-04  2.307e-04   1.969 0.049082 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8703 on 2411 degrees of freedom
Multiple R-squared:  0.7631,    Adjusted R-squared:  0.7569 
F-statistic: 121.4 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

avPlots(income.model.bc)

NA

NA

NA

NA
NA

BIC comparison before and after BoxCox transform

BIC(income.model.bc, income.model)

BIC(industry.model.bc, industry.model)

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)

clean_colname <- function(cols) {
  return(str_replace_all(cols, "[-'/ ,�&()`]", '_'))
}

#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  colnames(dummy_bc) <- clean_colname(colnames(dummy_bc))
  #colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "[-'/ ,�&()`]", '_')
  return(dummy_bc)
}

Cleaning column names further so stepwise regression doesn’t present any errors

#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
#colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)

#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
#colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)

Stepwise regression using BIC as the criteria (k = log(n)).

#Creating Stepwise Models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
model.fulls = list(income = lm(Avg.bc ~ ., data = income.dummy.bc), industry = lm(Avg.bc ~ ., data = industry.dummy.bc)) #All variables
model.emptys = list(income = lm(Avg.bc ~ 1, data = income.dummy.bc), industry = lm(Avg.bc ~ 1, data = industry.dummy.bc)) #intercept only
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  scope = list(lower = formula(model.emptys[[i]]), upper = formula(model.fulls[[i]]))
  n_obs = bc %>% dplyr::count() %>% dplyr::first()
  forwardBIC[[i]] = step(model.emptys[[i]], scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.fulls[[i]], scope, direction = "backward", k = log(n_obs))
}

Selecting Best Formula per Dataset from Stepwise Regressions

bic_func <- function (BIC.model){
  print('Adjusted R Squared:')
  print(summary(BIC.model)$adj.r.squared)
  print('Number of Coefficients:')
  print(dim(summary(BIC.model)$coefficient)[1])
  print('VIF Check: ')
  print(max(vif(BIC.model)))
  print("*************************")
  return(c(summary(BIC.model)$adj.r.squared, dim(summary(BIC.model)$coefficient)[1], max(vif(BIC.model))))
}

as.data.frame(rbind(c('income', 'forward', bic_func(forwardBIC[['income']])),
      c('income', 'backward', bic_func(backwardBIC[['income']])),
      c('industry', 'forward', bic_func(forwardBIC[['industry']])),
      c('industry', 'backward', bic_func(backwardBIC[['industry']]))
      )
) %>% select(dataset = V1, Stepwise = V2, `Adjusted R^2` = V3, `Number of Coefficients` = V4, `Maximum VIF` = V5) %>% write_csv('Shiny_app/data/stepwiseBIC_results.csv')

bic_func(forwardBIC[['income']])
bic_func(backwardBIC[['income']])
bic_func(forwardBIC[['industry']]) 
bic_func(backwardBIC[['industry']])

#Manual reduction of variables using VIF and then checked versus saturated model with Anova. This was not used because the saturated model contained multicollinearity issues as indicated by a high VIF score on some coefficients. And the anova test suggested that the coefficients removed in the reduced model were informative in our model, so we couldn't use it either. Thus Stepwise reduction is the preferred method for best model fit.

# VIF.variables <- as.data.frame(vif(model.fulls[['industry']])) %>% 
#   select(VIF = `vif(model.fulls[["industry"]])`) %>% 
#   filter(VIF > 5) %>% rownames()
# 
# industry.dummy.bc.VIF <- industry.dummy.bc %>% select(-all_of(VIF.variables))
# industry.model.VIF <- lm(Avg.bc ~ ., data = industry.dummy.bc.VIF)
# summary(industry.model.VIF)
# anova(industry.model.VIF, model.fulls[['industry']])

Best Model Selection from Stepwise

#The Best Models selected for both income and industry were forwardBIC.

#Income Group Dataset
income.best.formula <- forwardBIC[['income']]$call[[2]]
income.best.formula

#Industry Group Dataset
industry.best.formula <- forwardBIC[['industry']]$call[[2]]
industry.best.formula

Splitting data up into test data and training data (test data is for year 2019, training is the rest)

test_train_split <- function(dummy_bc, best.formula) {
  # data.test <- dummy_bc %>% filter(Year == 2019)
  # data.train <- dummy_bc %>% filter(Year != 2019)
  X <- model.matrix(best.formula, data = dummy_bc)[,-1]
  y <- as.matrix(dummy_bc %>% select(all.vars(best.formula)[1]))
  
  set.seed(0)
  train.i = sample(1:nrow(dummy_bc), 0.8*nrow(dummy_bc), replace = F)
  
  #train
  X.train <- X[train.i,]
  y.train <- y[train.i,]
  
  #test
  X.test <- X[-train.i,]
  y.test <- y[-train.i,]
  
  data.train <- as.data.frame(cbind(y.train, X.train))
  data.test <- as.data.frame(cbind(y.test, X.test))
  colnames(data.train)[1] = all.vars(best.formula)[1]
  colnames(data.test)[1] = all.vars(best.formula)[1]
  
  return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test, 'data.train' = data.train, 'data.test' = data.test, 'data' = dummy_bc))
}

Lasso regression for comparison to Forward Stepwise and Function to show metrics (R^2 and MSE) for Regularization (Ridge/Lasso)

regularization_func <- function (data, alpha, name){
  X.train <- data[['X.train']]
  y.train <- data[['y.train']]
  X.test <- data [['X.test']]
  y.test <- data[['y.test']]
  data.test <- data[['data.test']]
  # print(colnames(X.train))
  # print(colnames(X.test))
  # print(setdiff(colnames(X.train), colnames(X.test)))
  
  #create lambda grid
  lambda.grid = 10^seq(10, -10, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = alpha, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  # plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = alpha, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Alpha:", alpha, "Regression:", name))
  
  #Checking the best lambda
  # log(cv.lasso.models$lambda.min)
  # best.lambda <- cv.lasso.models$lambda.min
  # print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  # best.lambda.coeff <- predict(lasso.models, s = cv.lasso.models$lambda.min, type = "coefficients")
  # print('Number of Coefficients:')
  # print(dim(best.lambda.coeff)[1])
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = cv.lasso.models$lambda.min, newx = X.test)
  lasso.best.lambda.train.pred
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  print(paste('Dimensions of the Alpha:', alpha, ' Regression Coefficients for:', name))
  print(dim(coef(lasso.models))[1])
  p = dim(coef(lasso.models))[1]
  return(eval_results(y.test, lasso.best.lambda.train.pred, data.test, p)['Rsquare'])
}

Function for calculating adjusted R squared

# Calculate R squared from true values and predictions
eval_results <- function(true, predicted, df, p) {
  n = nrow(df)
  adj.RSS <- sum((predicted - true)^2)/(n-p-1)
  adj.TSS <- sum((true - mean(true))^2)/(n-1)
  adj.R_square <- 1 - adj.RSS / adj.TSS
  #RMSE = sqrt(RSS/n)
  
  return(c(Rsquare = adj.R_square))
}

Creates data structure that stores formulas and full,train, and test datasets for final model metric comparison

formulas <- list(income_cleaned = sat.formula, 
                 income_cleaned_bc = sat.formula.bc, 
                 income.data.split.sat = sat.formula.bc, 
                 income.data.split.best = income.best.formula,
                 industry_cleaned = sat.formula, 
                 industry_cleaned_bc = sat.formula.bc, 
                 industry.data.split.sat = sat.formula.bc, 
                 industry.data.split.best = industry.best.formula)

all.splits <- list(
  'income_cleaned' = test_train_split(income_cleaned, formulas[['income_cleaned']]),
  'income_cleaned_bc' = test_train_split(income_cleaned_bc, formulas[['income_cleaned_bc']]),
  'income.data.split.sat' = test_train_split(income.dummy.bc, formulas[['income.data.split.sat']]),
  'income.data.split.best' = test_train_split(income.dummy.bc, formulas[['income.data.split.best']]),
  'industry_cleaned' = test_train_split(industry_cleaned, formulas[['industry_cleaned']]),
  'industry_cleaned_bc' = test_train_split(industry_cleaned_bc, formulas[['industry_cleaned_bc']]),
  'industry.data.split.sat' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.sat']]),
  'industry.data.split.best' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.best']])
)

regularization_func(all.splits[['income_cleaned']], 0, 'income_cleaned')

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned"
[1] 54
    Rsquare 
-0.01019062 

Creating models for rsquared comparison

#For loops initialization
no.reg.r2 <- c() 
lasso.reg.r2 <- c()
ridge.reg.r2 <- c()


for (i in names(all.splits)) {
  #no regularization
  m = lm(formulas[[i]], all.splits[[i]][['data.train']])
  #no.reg.r2 <- c(no.reg.r2, summary(m)$adj.r.squared)
  y.predict = predict(m, newdata = as.data.frame(all.splits[[i]][['X.test']]))
  adj.R2 <- eval_results(all.splits[[i]][['y.test']], y.predict, all.splits[[i]][['data.test']], length(coef(m)))['Rsquare']
  no.reg.r2 <- c(no.reg.r2, adj.R2)
  
  #lasso regularization
  lasso.reg.r2 <- c(lasso.reg.r2, regularization_func(all.splits[[i]], 1, i))
  
  #ridge regularization
  ridge.reg.r2 <- c(ridge.reg.r2, regularization_func(all.splits[[i]], 0, i))
}

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income_cleaned"
[1] 54

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned"
[1] 54

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income_cleaned_bc"
[1] 54

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned_bc"
[1] 54

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income.data.split.sat"
[1] 54

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income.data.split.sat"
[1] 54

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income.data.split.best"
[1] 41

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income.data.split.best"
[1] 41

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry_cleaned"
[1] 65

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry_cleaned"
[1] 65

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry_cleaned_bc"
[1] 65

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry_cleaned_bc"
[1] 65

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry.data.split.sat"
[1] 65

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry.data.split.sat"
[1] 65

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry.data.split.best"
[1] 42

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry.data.split.best"
[1] 42

Adjusted R squared table for model comparison between Lasso, Ridge and No reg on cleaned, cleaned_bc, data.split.sat and data.split.best

df.rsquare <- as.data.frame(cbind('No Regularization' = no.reg.r2, 'Lasso' = lasso.reg.r2, 'Ridge' = ridge.reg.r2))
rownames(df.rsquare) = names(all.splits)
df.rsquare %>% tibble::rownames_to_column(var = 'Dataset') #%>% write_csv('Shiny_app/data/final_rsquare_table.csv')

Generating predictions using best model

Creating key dataframe for changes between user input colnames and dummy dataset colnames

user_input_pred %>% sapply(boxcox_to_dollars, USE.NAMES = T)

[1] 57857.47 45264.94 74016.44

For loop to create Master dataset with Industry and Income for true and predicted values of Avg.bc and Avg in Dollars

#For loop initialization list
joined.true.pred <- list('income' = NULL, 'industry' = NULL)
lambda.bcs <- list('income' = income.lambda.bc, 'industry' = industry.lambda.bc)

for (i in c('income', 'industry')) {
  data.index <- paste0(i, '.data.split.best')
  m <- lm(formulas[[data.index]], data = all.splits[[data.index]][['data']])
  
  #Making predictions using best model on our full dataset
  m.predict <- predict(m, newdata = all.splits[[data.index]][['data']])
  
  #Converting those target variable predictions from BoxCox transform back to Dollars
  lambda.bc <- lambda.bcs[[i]]
  predictions.df <- as.data.frame(m.predict) %>% 
    mutate(`Predicted Average in Dollars` = (m.predict*lambda.bc+1)^(1/lambda.bc)) %>% 
    tibble::rownames_to_column(var = 'Index')
  
  #Loading true values for join with predictions
  true.df <- all.splits[[paste0(i, '_cleaned_bc')]][['data']] %>% tibble::rownames_to_column(var = 'Index')
  
  #Joining the predicted data with the true dataset
  joined.true.pred[[i]] <- inner_join(predictions.df, true.df, by = 'Index')
  
  #Creating Master dataset with True Avg.bc, Predicted Avg.bc, True Average in Dollars and Predicted Average in Dollars for each Year, 
  #Credit Name and Income Group entry.
  joined.true.pred[[i]] <- joined.true.pred[[i]] %>% 
    mutate(`True Average in Dollars` = (Avg.bc*lambda.bc+1)^(1/lambda.bc)) %>% 
    relocate(`True Average in Dollars`, .before = `Predicted Average in Dollars`) %>% 
    relocate(Avg.bc, .before = m.predict) %>% 
    select(1:9, 
           `Predicted Avg.bc` = m.predict, 
           `True Avg.bc` = Avg.bc)
}
joined.true.pred[['income']]

joined.true.pred[['industry']]

combined.true.pred <- rbind(joined.true.pred[['income']] %>% mutate(dataset = 'income'), joined.true.pred[['industry']] %>% mutate(dataset = 'industry'))
combined.true.pred

Writing combined predicted and true values dataset to a csv file

combined.true.pred <- combined.true.pred %>% write_csv('Shiny_app/data/combined.true.pred.csv')

Visualizations of predictions and true values

Number of taxpayers per Group for a given Credit Name and Year input (Inputs in the filter)

income_cleaned %>% filter(Name == 'Investment Tax Credit', Year == 2019) %>% group_by(Year, Group) %>% summarise(sum(Num))

`summarise()` has grouped output by 'Year'. You can override using the `.groups` argument.